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Coupon collector's problem. In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more ...
Parimutuel betting. Parimutuel betting or pool betting is a betting system in which all bets of a particular type are placed together in a pool; taxes and the "house-take" or "vigorish" are deducted, and payoff odds are calculated by sharing the pool among all winning bets. In some countries it is known as the tote after the totalisator, which ...
Power Play 2× (1 in 2) Power Play 3× (1 in 3 1/3) Power Play 4× (1 in 10) Power Play 5× (1 in 10) Odds of winning [52] PB only $4 $8 $12 $16 $20 1 in 55.41 1 number plus PB $4 $8 $12 $16 $20 1 in 110.81 2 numbers plus PB $7 $14 $21 $28 $35 1 in 706.43 3 numbers; no PB $7 $14 $21 $28 $35 1 in 360.14 3 numbers plus PB $100 $200 $300 $400 $500
Different policy banks would offer different rates, though a payoff of 600 to 1 was typical. Since the odds of winning were 1000:1, the expected profit for racketeers was enormous. [41] The first modern government-run US lottery was established in Puerto Rico in 1934, [42] followed by New Hampshire in 1964.
In a typical 6/49 game, each player chooses six distinct numbers from a range of 1–49. If the six numbers on a ticket match the numbers drawn by the lottery, the ticket holder is a jackpot winner— regardless of the order of the numbers. The probability of this happening is 1 in 13,983,816. The chance of winning can be demonstrated as ...
Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
There are 13 possible payouts ranging from 1:1 to 2,400:1. The 1:1 payout comes every 8 plays. The 5:1 payout comes every 33 plays, whereas the 2:1 payout comes every 600 plays. Most players assume the likelihood increases proportionate to the payout. The one mid-size payout that is designed to give the player a thrill is the 80:1 payout.
A Dutch book or money pump is a set of bets that ensures a guaranteed loss, i.e. the gambler will lose money no matter what happens. [1] A set of beliefs and preferences is called coherent if it cannot result in a Dutch book. The Dutch book arguments are used to explore degrees of certainty in beliefs, and demonstrate that rational agents must ...